Question

What value of x for .
`\sqrt[5]{x}`will result in an integer between 2 and 5 inclusive?

Answer 1

For

`\sqrt[5]{x}`

The result of the square root will be an integer between 2 and 5 inclusive, symbolically:

`2\leq\sqrt[5]{x}\leq5`

Since the square root has to be an integer between these two numbers, the value of x will be a value between their values when powered by 5:

`\begin{gathered} 2^5\leq(\sqrt[5]{x})^5\leq5^5 \\ 32\leq x\leq3125 \end{gathered}`

x will be a value between 32 and 3125.